# Residual resultant over the projective plane and the implicitization problem

1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this article, we first generalize the recent notion of residual resultant of a complete intersection to the case of a local complete intersection of codimension 2 in the projective plane, which is the necessary and sufficient condition for a system of three polynomials to have a solution outside'' a variety, defined here by a local complete intersection of codimension 2. We give its degree in the coefficients of each polynomial and compute it as the gcd of three polynomials or as a product of two determinants divided by another one. In a second part we use this new type of resultant to give a new method to compute the implicit equation of a rational surface with base points in the case where these base points are a local complete intersection of codimension 2.
Type de document :
Communication dans un congrès
Internation Symposium on Symbolic and Algebraic Computing (ISSAC), Jul 2001, London, Ontario, Canada. ACM, pp.48--55, 2001
Domaine :

Littérature citée [22 références]

https://hal.inria.fr/inria-00099846
Contributeur : Laurent Busé <>
Soumis le : mardi 26 septembre 2006 - 09:43:18
Dernière modification le : vendredi 12 janvier 2018 - 01:48:44
Document(s) archivé(s) le : jeudi 20 septembre 2012 - 10:56:14

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• HAL Id : inria-00099846, version 1

### Citation

Laurent Busé. Residual resultant over the projective plane and the implicitization problem. Internation Symposium on Symbolic and Algebraic Computing (ISSAC), Jul 2001, London, Ontario, Canada. ACM, pp.48--55, 2001. 〈inria-00099846〉

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